For an oriented virtual link, L.H. Kauffman defined the f polynomial (Jones polynomial). The supporting genus of a virtual link diagram is the minimal genus of a surface in which the diagram can be embedded. In this paper we show that the span of the f -polynomial of an alternating virtual link L is determined by the number of crossings of any alternating diagram of L and the supporting genus o...

Given a set of spheres in 3D, constructing its Voronoi diagram in Euclidean distance metric is not easy at all even though many mathematical properties of its structure are known. This Voronoi diagram has been known for many important applications from science and engineering. In this paper, we characterize the Voronoi diagram of spheres in three-dimensional Euclidean space, which is also known...

Constructing phase diagram and its subsequent quality lines for lean gas condensate reservoirs is always crucial and challenging topic in reservoir fluid studies. Due to small amounts of liquid drop-outs in lean gas condensates at reservoir conditions, full experimental tracking of phase diagram and its relevant quality lines is almost impossible for lean gas condensates.On the other hand, ...

The concept mapping and the Vee diagram are important tools for improving the level of conceptual learning of mathematics in all educational levels that can play an important role in the learner's achievement. The purpose of this study is to use a concept mapping and Vee diagram, to calculate the volume of an object by the integral, includes the reaction of what a teacher really knows, the way ...

A binary moment diagram, which was proposed for arithmetic circuit verification, is a directed acyclic graph representing a function from binary-vectors to integers (f : {0, 1}n → Z). A multiplicative binary moment diagram is an extension of a binary moment diagram with edge weights attached. A multiplicative binary moment diagram can represent addition, multiplication and many other functions ...

Recently a new metaphor for diagramming, the intelligent diagram has emerged. This new metaphor provides an excellent basis for diagram beautification since it automatically collects geometric constraints which capture the semantics of a diagram during diagram construction. By applying visual-language-specific layout rules which impose additional desired constraints on the diagram component pla...

To determine the value of perfect informa­ tion in an influence diagram, one needs first to modify the diagram to reflect the change in information availability, and then to com­ pute the optimal expected values of both the original diagram and the modified diagram. The value of perfect information is the dif­ ference between the two optimal expected values. This paper is about how to speed up ...

In this paper, we introduce the fuzzy Voronoi diagram as an extension of the Voronoi diagram. We assume Voronoi sites to be fuzzy points and then define the Voronoi diagram for this kind of sites, then we provide an algorithm for computing this diagram based on Fortune’s algorithm which costs O(n log n) time. Also we introduce the fuzzy Voronoi diagram for a set of fuzzy circles, rather than fu...

ground water and surface water create a range of problems in lignite mining utilizing surface mining methods. in order to create a safe and economic mining environment, it is essential to carry out mining after dewatering the rock mass surrounding the lignite mines by advance dewatering techniques. this paper briefly describes the ground water regimes including pressure gradients associated wit...